92=9x^2+6x

Solution for 92=9x^2+6x equation:

92=9x^2+6x

We move all terms to the left:

92-(9x^2+6x)=0

We get rid of parentheses

-9x^2-6x+92=0

a = -9; b = -6; c = +92;
Δ = b2-4ac
Δ = -62-4·(-9)·92
Δ = 3348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3348}=\sqrt{36*93}=\sqrt{36}*\sqrt{93}=6\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{93}}{2*-9}=\frac{6-6\sqrt{93}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{93}}{2*-9}=\frac{6+6\sqrt{93}}{-18}
$